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Math Help - inequality in quadrilateral

  1. #1
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    inequality in quadrilateral

    In convex quadrilateral ABCD, K is midpoint of AB, M is midpoint CD,. Prove that $ KM \le \frac{BC+AD}{2} $.
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    Quote Originally Posted by olkaabc View Post
    Prove that $ KM \le \frac{BC+AD}{2} $.
    Huh?
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  3. #3
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    Quote Originally Posted by olkaabc View Post
    In convex quadrilateral ABCD, K is midpoint of AB, M is midpoint CD,. Prove that  KM \le \frac{BC+AD}{2} .
    We know that \frac{1}{2}\overrightarrow {AB}  + \overrightarrow {BC}  + \frac{1}{2}\overrightarrow {CD}  = \overrightarrow {KM} and -\frac{1}{2}\overrightarrow {AB}  + \overrightarrow {AD}  - \frac{1}{2}\overrightarrow {CD}  = \overrightarrow {KM}

    If you add those two together and divide by two, what do get?
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